Because you are moving with an enormous speed, your mission from the previous problem A.1 will be influenced by the eects of time dilation described by special relativity: Your spaceship launches in June 2020 and returns back to Earth directly aer arriving at Sirius. (a) How many years will have passed from your perspective? (b) At which Earth date (year and month) will you arrive back to Earth?
Answers
Because you are moving with an enormous speed, your mission from the previous problem A.1 will be influenced by the eects of time dilation described by special relativity: Your spaceship launches in June 2020 and returns back to Earth directly aer arriving at Sirius. (a) How many years will have passed from your perspective? (b) At which Earth date (year and month) will you arrive back to Earth?
Explanation:
a) The time for the astronauts going to space will be :
t=\frac{D}{v}=\frac{8.7c}{0.7c}=12.42\text{ y (12 y 153 d)}.t=
D /v
= 8.7c / 0.7c
=12.42 y (12 y 153 d).
From June 2020 it will be November 2032.
(b) It will take (for people on Earth) :
t_e=\frac{t}{\sqrt{1-(v/c)^2}}=\frac{12.42}{\sqrt{1-(0.7)^2}}=17.39\text{ y (17 y 142 d)}.t e
= 1−(v/c) ² t =² 12.42 / √ 1−(0.7) ²
=17.39 y (17 y 142 d).
From June 1, 2020 it will be October 21, 2037.
You will arrive back on earth in October 21, 2037.